Accepted Answer

Your going to need to use the Fish Hook. Go to the the shop in World 3 that sells the blue doors, and use one on the ledge south of the shop. There you should find the hook. In the battle with the Cheep Cheep, use the hook as soon as he jumps in the water and heals himself. That should fish him out. Then you have to pummel away at him quickly, before he grows too big and blows up, dealing 99 damage.